obtaining knowledge of genes behavior in genetic...

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Obtaining Knowledge of Genes’ Behavior in Genetic Regulatory System by Utilizing

Multiagent Collaborative Computation

Adang Suwandi Ahmad1 and Arwin Datumaya Wahyudi Sumari2

1School of Electrical Engineering and Informatics, Institut Teknologi Bandung,

Achmad Bakrie Building, 2nd Floor, Jl. Ganeca 10, Bandung, 40132,

2Department of Electronics, Indonesian Air Force Academy,

Jl. Laksda Adisutjipto, Yogyakarta, 55002

Indonesia

1. Introduction

All living organisms are built from millions of cells that work together in a very systematic

manner. The trait of each organism is determined by the cells. The function of a living cell is

performed by a sequence of well-coordinated activities by a large number of genes. The

gene itself is a sequence of Deoxyribonucleic Acid (DNA). The products of a cell are made

by the proteins synthesized in accordance with the instructions contained in the DNA

(Willett, 2006) since it encodes all the information required for the development and

functioning of an organism (Emmert-Streib & Dehmer, 2008).

The expression of a gene is a biological process which a DNA sequence is translated to

become a protein. The protein is an important molecule for determining the structure,

mortality, metabolism, signaling, reproduction, etc. of a cell. Some genes influence how

other gene or genes are expressed. Modifying genes may change the affect of other genes.

The expression of a gene or genes is regulated by a mechanism called Genetic Regulatory

System (GRS). The GRS’ task is to control whether genes are active or inhibit.

Of ways for understanding and analyzing the behavior of GRS is by using microarray

data. Microarray is sets of miniaturized reaction areas that may also be used to test the

binding of DNA fragment (Reece, 2004). and it exploits the preferential binding of

complementary nucleic acid sequences to simultaneously measure expression levels of

thousands of genes (Dill, Liu, & Grodzinski, 2009). By having knowledge regarding the

influence of a gene or genes to the others in microarray data, we can make estimations of

the genes behavior in GRS in order to obtain better products in the future. According to

(Ewens & Grant, 2005), there are three basic questions that can be answered by using

microarray data:

a. What genes are expressed in a given sample?

b. Which genes are differentially expressed between different samples?

c. How can one find different classes, or clusters, of genes which are expressed in a

correlated fashion across a set of samples? How can one find different classes of

samples based on their gene expression behavior?

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In this paper we address the utilization of Multiagent Collaborative Computation (MCC) to

model the genes’ interactions in GRS to address questions (a) and (b). Simply, each gene will

be represented by an agent that performs internal activities and performs communications

with other genes as occurred in biological genes. On each interaction time, we can have

knowledge regarding individual gene expressiveness and all genes behavior. The process in

obtaining this knowledge will be carried out by Knowledge-Growing System (KGS) based

on Observation Multi-time Arwin-Adang-Aciek-Sembiring (OMA3S) information-

inferencing fusion and the results will be compared to the MCC results. The comparison

has also been done to ensure the accuracy of the KGS-based MCC results. In our research,

we use data of yeast cycle database taken from [6] as the case study. The rest of the paper is

structured as follows. The concept of MCC and a review of the state-of-the-art of GRS

research will be delivered in Section 2. In Section 3, we present the concept of KGS as well as

OMA3S method that is used as its knowledge-growing mechanism. The utilization of MCC

to GRS as well as the knowledge production by KGS will be delivered in Section 4. Finally,

the paper is concluded in Section 5 with some concluding remarks.

2. State-of-the-art of genetic regulatory system research and the concept of multiagent collaborative computation

2.1 State-of-the-art on genetic regulatory system research The research, studies, and experiments on GRS have been done widely all over the world.

These efforts are aimed to one objective, namely how to obtain the most suitable model in

order to present the mechanism occurs in GRS. In these endeavors, there are two approaches

that have been carried out as studied comprehensively by (Ahmad & Sumari, 2009a) as

follows.

In the first approach the GRS mechanism is directly modeled by utilizing available methods

such as Dynamic Bayesian Network (DBN) based on knowledge growing, weight matrices,

petri nets, artificial gnome model, Neural Network (NN) or its combination with fuzzy

technique such as Evolving Connectionist System (ECOS), piece-wise linear, Boolean, and

power graph analysis.

The second one is to model the GRS by inferring its structure utilizing techniques such as

best-fit extension problem, linear programming combined with supervised learning

framework, DBN, evolutionary computation, graph and Linearized Additive Model (LAM),

steady-state gene expression, Dynamic Differential BN (DDBN), combination of DBN with

Reversible Jump Markov chain Monte Carlo (RJMCC) or with Greedy search algorithm and

Markov Chain Monte Carlo (MCMC), Bayesian and MCMC, iterative algorithm based on

epistemic approach of conjecture and refutation, NN, and combination of clustering

techniques with NNs.

At the time of the writing of this paper, we have not found literatures that study methods in

obtaining knowledge regarding the behavior of genes in GRS in order to estimate their

expression in the future especially that utilizes multiagent approach. This is the primary

matter that will be discussed in this paper. Our hypothesis is by accurately estimating the

GRS behavior in the future we can carry out anticipation actions in order to prevent the

negative expression of genes that can cause negative effects to living organisms.

2.2 Multiagent collaborative computation MCC is a new paradigm in MultiAgent System (MAS). It is the emulation of how human

beings work in collaborative manner in solving problems or finding solutions of given

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Obtaining Knowledge of Genes’ Behavior in Genetic Regulatory System by Utilizing Multiagent Collaborative Computation

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problems or in achieving a common or joint goal or objective, by sharing resources they

have for the successfulness of their work. Working in collaborative manner does not need

leader. What it needs is a divider agent for dividing the work or task to be solved or given

into subworks or subtasks, and distributes them to some collaborative agents, and a fusion

agent that is tasked to fuse the results from collaborative agents to obtain a comprehensive

result or joint goal. By doing it, the subworks can be processed in parallel manner to

achieve the subgoals, and therefore it can save the processing time. Before we go deeper

into MCC, we start this section with the reintroduction of the concept of agent and the

concept of collaborative computation as well as its merit.

a. The Concept of Agent (Ahmad & Sumari, 2008)

There have been many literatures that study agent, but in this section we view an agent from a

comprehensive perspective. In real life, agent is defined as a thing that causes a significant

effect on a situation. In order to give this effect, agent must have capabilities. “Capability” in

this circumstance is the ability to manage when the tasks will be carried out, knows where to

move, knows how to do the tasks, knows the success level of the tasks being carried out, and

the consequences of the tasks being done. The essential thing that enables the agent in

performing its activities is the brain, a place where the information processing is carried out.

This is the most grandeur that is not possessed by other living things.

In accomplishing the assigned tasks, the agent always senses its surrounding environment

to get as much as information that can affect its activities. The gathered information is

processed in its brain, combining it with the existing information, making inferencing on the

fused information, performing information-inferencing fusion, and making the best decision

for actions to be done in anticipating the environment dynamics. The relation of an agent

with its surrounding environment as well as its information processing mechanism is

simply depicted in Fig. 1.

Fig. 1. The concept of agent along with its information-inferencing fusion capability

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In many literatures, agent is stated must have an intelligent characteristic. However, because

there is no uniform definition of what agent is, one common consensus is taken that the

autonomy or we call this as self-governing, as its the essential characteristic. Self-governing

means the agent has capability to instruct itself to accomplish the tasks and do self-evaluation

to value the success rate of the assigned tasks accomplishment for future enhancement.

b. The Concept of Collaborative Computation

Collaboration is taken from the Latin word “collaborare” meaning “to work together” , while

“collaborative” is an adjective form of “collaboration” . So, collaboration is defined as to

work with another or others on a joint project or in deeper definition is a process in which

Fig. 2. The concept of collaborative computation in a group of agents (Sumari & Ahmad, 2009)

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entities share information, resources and responsibilities to jointly plan, implement, and

evaluate a program of activities to achieve a common goal (Camarinha-Matos &

Afsarmanesh, 2008).

In collaborative scheme, a group of entities enhance the capabilities of each other that

implies in sharing risks, resources, responsibilities, and reward. Collaboration involves

mutual engagement of participants to solve a problem together, which implies mutual trust

and thus takes time, effort, and dedication. On the other side, “computation” is defined as a

calculation involving numbers or quantities. By employing computational approach, we can

manipulate a large database to solve problems at hand very fast. The consequence is faster,

more complete, and more accurate results than that can be achieved by conventional

approach.

By combining the two definitions previously explained, we define “collaborative

computation” as a calculation on quantities done by a group of agent or multiagent that

works together to achieve common or joint goals (Ahmad, Sumari, & Zubir, 2009) as

depicted in Fig. 2. In an MCC scheme, each agent in the collaborative framework performs

its own tasks to achieve its own goals. The goals achieved by each agent actually are partial

parts of joint goal, which is the combination of partial goals. In simple word, the system is

given a problem along with the goal that has to be achieved. The problem is then divided

into several sub-problems that have to be solved by the agents. In achieving the sub-goals,

the agents perform computation in parallel. The achieved sub-goals are then combined to

become a single comprehensive goal that is called as joint goal (Sumari & Ahmad, 2009).

c. The Merits of Multiagent Collaborative Computation Approach (Sumari, 2010)

Fig. 3. The concept of MCC (Sumari, 2010)

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GRS is a very complex structure that regulates millions of genes in living organism’s body.

We believe that multiagent approach is suitable to model the genes’ interactions in GRS

with some strong reasons. MAS is aimed to cope with large-scale, realistic, and complex

problems that cannot be handled by single agent in order to find a solution of global

problems or to regulate or control complex systems. In MCC framework, the given task will

be divided into subtasks according to each agent specific task. By performing this, the

information processing can be done in simultaneous manner by all agents so that the

processing time can be reduced to minimum.

Assume that we have n agents in MCC framework. Given a task that a single agent can

process it in t time. If the task is divided into n subtasks and distributed them to n agents,

theoretically, the result of the process can be obtained in t/ n time with total t/ n +τ where τ is the time reserved for dividing the task and fusing or combining the subgoals into a joint

goal or the ultimate result. Therefore, by utilizing MCC the information-processing time can

be reduced from t to t/n+τ , or (t/n+τ) <t. This mechanism is illustrated in Fig. 3.

3. Knowledge-growing system and OMA3S information-inferencing fusion method

3.1 What is knowledge-growing? (Sumari et.al, 2010a) It is not easy to find any literature that defines or describes what the term “Knowledge-

Growing” is. The only research that used this term was for industrial application, that is,

examined how the knowledge growing old in human brain and used the analogy of it for

building a reconfiguration system for car application. It concentrated on the optimization of

knowledge retrieval rather than emulating the way of human brain grows the knowledge

over time, and used actuality measurement to measure the knowledge that is very often

used to solve an actual problem.

Up to the writing of this paper, there is no research that examines and develops an

intelligent method for an intelligent system that emulates the mechanism how the

human brain grows the knowledge from time to time. Our approach in developing KGS

was started from our observation to an intelligence characteristic displayed by human

brain in performing such matter by fusing information perceived by human sensory

organs and deliveres it to the brain. This approach is discussed in detail in (Ahmad &

Sumari, 2008). The original concept of information fusion, even though it also adopted

the mechanism occurs in living things’ brain, it is just defined how to fuse the

information for making estimation regarding a phenomenon, see (Hall & Llinas, 2001)

for the detail.

3.2 The concept of KGS Essentially, KGS is a system that is capable of growing its knowledge along with the

accretion of information it receives as the time passes (Ahmad & Sumari, 2009b). The

concept of KGS emerges from the observation of the mechanism occurs in human brain

when performing information-inferencing fusion to obtain new knowledge. In order to have

a more depth understanding on this mechanism, we developed a model of Human Inference

System (HIS) as the basis for our model of KGS as depicted in Fig. 4. The general formula to

obtain the number of inferencing is presented in (1).

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( )2 1= − −δλ δ (1)

with λ is the number of inferencing from fused information and δ is the number of

information sources or sensors.

Fig. 4. A simplified illustration of human inference system (Sumari et.al, 2010b)

3.3 Knowledge growing mechanism As we can see in Fig. 4, the process in obtaining new knowledge from the gathered-and-

delivered information of a phenomenon observed by the sensory organs will have to get

through a five-step process, i.e. information fusion, information inferencing, information-

inferencing fusion, knowledge inferencing, and knowledge-inferencing fusion. Based on the

HIS model, we developed the mechanism that will be occurred in our model of KGS as

depicted in Fig. 5.

New knowledge in this scheme is called as information with Degree of Certainty (DoC)

whcih is introduced by (Sumari et.al, 2009b), that is, a value that determines the certainty of

the new knowledge regarding the observed phenomenon is considered accurate. Term “γ” is

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the representation of the time needed to obtain the new knowledge. The DoC is obtained by

applying A3S (Arwin-Adang-Aciek-Sembiring) method (Ahmad & Sumari, 2008).

Fig. 5. The mechanism of growing the knowledge in KGS as the representation of Fig. 4

(Sumari et.al, 2009a)

3.4 OMA3S information-inferencing fusion method To grow the knowledge, the requisites that have to be fulfilled are there has to be a

knowledge base and fusion mechanism. The fusion will be applied to the received

information with the existing or prior information/ knowledge. The knowledge is the result

of the combination between the new information and the existing one which is called as

after-processed information or posterior information. The mature technique for this

situation is Bayes Inference Method (BIM) (Hall, 1992), a special case of probability theory.

For performing the information-inferencing fusion, we have developed a method called A3S

information-inferencing fusion which is aimed to improve BIM for managing multi-

hypothesis multi-indication problems (Ahmad & Sumari, 2008). The A3S version which

involves the time parameter in the computation is called OMA3S (Sumari et.al, 2009c). The

detail how this method works is illustrated in Table I followed by its paired equations given

in (2) and (3).

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( ) ( )11

==∑ j

ij iP

P

δ υψ δ (2)

( ) ( )1⎡ ⎤= ⎣ ⎦Y j

estimateP Pψ ψ (3)

with ( )1

jP ψ is New-Knowledge Probability Distribution (NKPD), ( )j

iP υ is information j

from sensor i, while 1= ,...,i δ is the number of sensor and 1= ,...,j λ is the number of fused

information. The ( )1

jP ψ and 1 ∈Ψjψ is the representation of “ fused information” of the

information delivered from multi-sensor. The word “estimated” means the selected fused

information is the most likely inferencing/ knowledge from all available

inferencing/ knowledge given information from multi-sensor. ( )estimate

P ψ is the largest

value of ( )1jP ψ that is called as DoC and [ ] [ ]

1==Y,...,

... max ...j m

. Term ( )1jP ψ defines NKPD at

1=γ .

Probability Distribution of Information from thi Sensor

and Probability Distribution of thj Fused Information Information

from -th

Sensor 1 2 3 … j … λ

1 ( )1iP υ ( )2

iP υ ( )31P υ … ( )1

jP υ … ( )1P λυ

… … … … … … … …

i 0 0 ( )3iP υ … ( )j

iP υ … ( )iP λυ

… … … … … … … …

δ 0 0 0 … 0 … ( )P λδυ

ψ (DoC) ( )11P ψ ( )2

1P ψ ( )31P ψ … ( )1

jP ψ … ( )1P λψ

Table 1. The illustration of the computation mechanism of A3S information-inferencing

method

Next observations on the same phenomenon will result in new NKPD at next time series

and these NKPD will form NKPD over Time (NKPDT) as presented in (4) and (5).

( ) ( )1

Γ

== Γ∑ j

j

P

P

γγφ

θ (4)

( ) ( )⎡ ⎤= ⎣ ⎦Y jestimateP Pθ θ (5)

with ( )j

tP θ is NKPDT, ( )j

tP ψ is information j observed at observation time γ , while

1= Γ,...,γ is the number of observation time and 1= ,...,j λ is the number of fused

information. The ( )jP θ and ∈Θjθ is the representation of “knowledge” of the information

delivered from multi-sensor at observation time γ . ( )estimate

P θ is the value of DoC of ( )jP θ

or the ultimate knowledge after a certain observation time.

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3.5 Measuring KGS-based MCC’s degree of certainty The KGS-based MCC’s certainty of the phenomenon it observes is measured by using DoC

in (6)

( ) 1= − j

estimateDoC P θ φ (6)

where 1= ,...,j λ and 1jφ is the knowledge in term of probability value of the j best

hypothesis at observation time 1γ .

4. The utilization of KGS-based MCC to GRS

4.1 GRS database In this research we use five kinds of yeast25 database as presented in Table 2.

Database Type Number of Gene Time Sequence (t)

Alpha 25 18

Cdc15 25 24

Cdc28 25 17

Cho 25 17

Yeast25

Elu 25 18

Table 2. Yeast25 database for validating KGS-based MCC

As previously mentioned in earlier section, the genes regulated by GRS will be represented by

agents that will be working together in MCC paradigm. The experiments and the results

delivered in this section are taken from (Sumari, 2010). We use data from (Zubir, 2009) namely

yeast25-cho database as presented in Table 2. In this database, there are 25 genes from ACE2 to

SIC1 as listed in column 1 with an interaction time interval from t-1 to t-17 or 17t times as

shown in line 1. In order to give a view on the challenge in obtaining the knowledge

regarding what genes are expressed in a given sample as well their behavior in a certain

interaction time, the complexity of the data given in Table 3 is depicted in Fig. 6 and Fig. 7.

The expressiveness of individual genes in 17t of interaction time is presented in Fig. 6, while

the genes behavior in 17t of interaction time is presented in Fig. 7. The challenge in this case is

to obtain knowledge from this phenomenon to answer the questions raised in Section 1.

Gene/Time t1 t2 t3 t4 t5 t6 t7 t8 t9

ACE2 148 113 144 209 319 360 434 411 462

ASH1 380 256 201 256 320 327 245 366 795

FKH1 52 64 67 167 330 348 227 177 167

MBP1 360 326 321 425 502 484 487 410 401

MCM1 1350 1815 2095 1835 1907 1861 1734 1991 1446

NDD1 210 150 312 409 394 413 322 292 234

STB1 78 123 226 145 54 53 47 11 75

SWI4 87 115 183 104 79 77 71 88 101

SWI5 121 167 272 268 323 540 634 591 606

SWI6 421 520 699 846 869 853 740 721 558

ALG7 97 70 156 168 153 137 164 112 124

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CDC20 93 235 325 208 108 168 158 124 145

CDC21 17 59 106 93 57 37 18 18 19

CDC5 86 106 89 154 219 367 549 602 480

CDC6 554 471 967 930 936 876 809 831 864

CLB2 92 158 122 145 259 348 489 554 422

CLB5 562 785 1756 949 659 612 467 563 455

CLN1 149 1045 1344 1305 998 1013 717 571 323

CLN2 445 1620 2485 1303 916 808 738 636 303

CTS1 552 1080 447 258 287 466 435 299 217

EGT2 989 1244 732 786 1083 1284 816 678 1293

FAR1 235 263 160 165 303 468 429 880 903

HTA1 905 810 1490 1594 2037 999 1178 976 843

PCL2 153 510 620 260 224 235 157 130 238

SIC1 352 295 355 308 361 356 294 212 541

Table 3a. Genes’ names and their interaction values over time for yeast25-cho from t1 to t9

(continued to Table 3b)

Gene/Time t10 t11 t12 t13 t14 t15 t16 t17

ACE2 398 226 187 325 433 343 466 344

ASH1 1862 1180 640 544 388 327 517 959

FKH1 91 74 118 172 194 163 144 106

MBP1 277 341 364 507 467 484 473 382

MCM1 2227 1945 1334 1179 1830 1506 1517 1440

NDD1 198 215 319 365 333 246 250 238

STB1 120 140 129 98 66 45 75 44

SWI4 191 172 134 111 74 43 70 83

SWI5 540 463 357 449 937 743 1024 659

SWI6 651 758 641 741 887 885 744 692

ALG7 124 151 170 202 186 172 155 70

CDC20 160 172 166 175 111 113 112 112

CDC21 28 82 90 89 36 19 12 15

CDC5 238 219 202 324 326 435 496 471

CDC6 1149 902 689 859 799 832 707 921

CLB2 236 185 151 218 267 365 350 365

CLB5 1207 1325 643 647 657 509 464 508

CLN1 1152 1870 1388 989 1074 769 614 601

CLN2 791 1288 1624 1035 839 687 868 433

CTS1 1161 1840 1181 830 979 828 507 553

EGT2 4297 3430 3240 1598 1355 1044 2123 1813

FAR1 1794 1437 725 535 570 621 739 1194

HTA1 1934 1815 1998 1103 1888 2346 1708 1580

PCL2 428 659 409 284 276 178 203 211

SIC1 1286 813 595 490 398 400 389 692

Table 3b. Genes’ names and their interaction values over time for yeast25-cho from t10 to t17

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Fig. 6. The expressiveness of individual genes in 17t of interaction time (Sumari, 2010)

Fig. 7. The genes behavior in 17t of interaction time (Sumari, 2010)

4.2 The KGS-based MCC’s task and objective In this situation the task of KGS-based MCC is to carry out computation to obtain values of

genes behavior in a unity and individual genes expressiveness in an interval of interaction

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time. Its objective is to obtain DoCs based on those obtained values to show genes behavior

in a comprehensive manner and to find out the most expressive genes, that is, the most

probable genes that give big influence to the product of their interaction. Therefore, for this

purpose we create a strategy as follows. • First, represent the genes into agents in multiagent system and construct the MCC framework for it. • Second, represent the genes’ interaction values into two-value state namely active and

inhibit, where an active gene will be assigned binary value ‘1’ and binary value ‘0’ if it is inhibited or not active. • Third, observe the genes’ interaction state in time-by-time manner and put arcs on the

genes which relate to each other as the representation of the existence of communication amongst agents. In this case only the active ones. Carry out this procedure until the last t in time series. During the interaction time, agents apply OMA3S method to obtain knowledge in collaborative manner. The result will be

system’s knowledge at certain interaction time t. • Fourth, obtain the inferencing of the KGS-based MCC behavior as the representation of genes behavior in biological GRS. This inferencing will become the ultimate knowledge

obtained by the system.

a. The Representation of Genes into MCC Structure

Fig. 8. The representation of genes of yeast25-cho by means agents in MCC structure

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We assume that the task divider agent is already done its task and produces Table 2. Refer

to Figure 3 in Section 2.2 we can simply convert the genes of yeas25-cho into agents in MCC

structure as follows. The first and the last genes in the list namely gene ACE2 and gene SIC1

are represented by agent i and agent n where i = 1,…,n and n = 25. The structure of the MCC

is depicted in Fig. 8.

b. The Representation of Genes’ Interaction Values into Two-Value State

The simplest means to represent the existence of the interaction among genes is by

representing them with value ‘1’ for ‘active’ interaction and ‘0’ for ‘inhibit‘ interaction as alsi

done by (Pasanen and Vihinen, 2005). This is what is called as Boolean representation of

genes interaction in GRS. We realize that each gene has its own highest and lowest value

that cannot be treated identically one to another. In order to minimize the chances of error in

collaborative computation process, we use the threshold-value equation as presented in (7).

1

1

1

0

=

=

⎧⎪⎪ <⎪= ⎨⎪⎪ ≥⎪⎩

∑∑

,

,

i

i i

i

i

i i

if

if

λτ

ττ λ

ττ

ψψ λφ

ψψ λ

(7)

with ∈Πiτφ is a binary-sequence which represents a set of interaction value at observation

time t, iτψ is the interaction value of agent j at observation time t, and τ is the number of

interaction sequence t when the observation is carried out. The parameter t in this case is

dimensionless. The application of (7) to the data given in Table 3 is presented in Table 4.

Gene/Time t1 t2 t3 t4 t5 t6 t7 t8 t9

ACE2 1 1 1 1 0 0 0 0 0

ASH1 1 1 1 1 1 1 1 1 0

FKH1 1 1 1 0 0 0 0 0 0

MBP1 1 1 1 0 0 0 0 1 1

MCM1 1 0 0 0 0 0 0 0 1

NDD1 1 1 0 0 0 0 0 0 1

STB1 1 0 0 0 1 1 1 1 1

SWI4 1 0 0 1 1 1 1 1 1

SWI5 1 1 1 1 1 0 0 0 0

SWI6 1 1 1 0 0 0 0 0 1

ALG7 1 1 0 0 0 1 0 1 1

CDC20 1 0 0 0 1 0 0 1 1

CDC21 1 0 0 0 0 1 1 1 1

CDC5 1 1 1 1 1 0 0 0 0

CDC6 1 1 0 0 0 0 1 0 0

CLB2 1 1 1 1 1 0 0 0 0

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CLB5 1 0 0 0 1 1 1 1 1

CLN1 1 0 0 0 0 0 1 1 1

CLN2 1 0 0 0 1 1 1 1 1

CTS1 1 0 1 1 1 1 1 1 1

EGT2 1 1 1 1 1 1 1 1 1

FAR1 1 1 1 1 1 1 1 0 0

HTA1 1 1 0 0 0 1 1 1 1

PCL2 1 0 0 1 1 1 1 1 1

SIC1 1 1 1 1 1 1 1 1 0

Table 4a. The conversion results of genes interaction values from Table 2a (continued to

Table 4b)

Gene/Time t10 t11 t12 t13 t14 t15 t16 t17

ACE2 0 1 1 0 0 0 0 0

ASH1 0 0 0 1 1 1 1 0

FKH1 1 1 1 0 0 0 1 1

MBP1 1 1 1 0 0 0 0 1

MCM1 0 0 1 1 0 1 1 1

NDD1 1 1 0 0 0 1 1 1

STB1 0 0 0 0 1 1 1 1

SWI4 0 0 0 0 1 1 1 1

SWI5 0 1 1 1 0 0 0 0

SWI6 1 0 1 0 0 0 0 1

ALG7 1 0 0 0 0 0 0 1

CDC20 0 0 0 0 1 1 1 1

CDC21 1 0 0 0 1 1 1 1

CDC5 1 1 1 0 0 0 0 0

CDC6 0 0 1 0 1 0 1 0

CLB2 1 1 1 1 1 0 0 0

CLB5 0 0 1 1 1 1 1 1

CLN1 0 0 0 0 0 1 1 1

CLN2 1 0 0 0 1 1 1 1

CTS1 0 0 0 0 0 0 1 1

EGT2 0 0 0 1 1 1 0 0

FAR1 0 0 0 1 1 1 0 0

HTA1 0 0 0 1 0 0 0 0

PCL2 0 0 0 1 1 1 1 1

SIC1 0 0 0 0 1 1 1 0

Table 4b. The conversion results of genes interaction values from Table 2b

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c. The Observation to Agents Interaction and Obtaining Knowledge from It

Some influence graphs will be presented to show the interaction amongst KGS-based MMC

agents in GRS, and knowledge that is acquired by all agents collaboratively at 1t , 6t and

after 6t , at 17t and after 17t . The expressiveness of single agents and their behaviour at a

certain time and at a certain time interval such as from 1t to 6t are depicted in Fig. 9 to Fig.

15, while for all 17t of interaction time is presented in Fig. 16.

Fig. 9. Influence graph of KGS-based MCC behaviour at 1t . Yellow colour represents the

active agents during the interaction at that time

Fig. 10. Knowledge acquired by agents at 1t .

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Fig. 11. Influence graph of KGS-based MCC behaviour at 6t

Fig. 12. Knowledge acquired by agents at 6t

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Fig. 13. Knowledge acquired by agents after 6t of interaction time

Fig. 14. Influence graph of KGS-based MCC behaviour at 17t

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Fig. 15. Knowledge acquired by agents at 17t

Fig. 16. Knowledge acquired by agents after 17t of interaction time

d. Knowledge Obtained by KGS-based MCC

The computation results in form of the values of DoCs that are produced by KGS-based

MCC’s fusion agent which are compared with the number of communication paths formed

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during agents interaction is presented in Fig. 17 and Fig. 18. These DoCs become the

ultimate knowledge of the system.

Fig. 17a. The ultimate knowledge acquired by the system regarding individual agents

expressiveness after 17t of interaction time. The DoCs of the system’s knowledge are

compared with the communication paths formed amongst agents

Fig. 17b. 3D line graphic representation of system’s knowledge regarding individual agents

expressiveness after 17t of interaction time

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Fig. 18a. The ultimate knowledge acquired by the system regarding all agents behavior

during 17t of interaction time

Fig. 18b. 3D line graphic representation of the system’s knowledge regarding all agents

behavior during 17t of interaction time

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496

After observing Fig. 17 and Fig. 18, we can have knowledge regarding KGS-based MCC

agents’ behaviour as follows.

1. Viewed from individual agents expressiveness we can obtain knowledge that gene

ASH1 exhibit a dominant role even though there are genes CLB5, EGT2, and PCL2 that

also show their expressiveness with DoC = 0.053. The certainty that gene ASH1 is the

most expressive gene amongst other expressive genes is shown by the difference

between DoC and the number of weighted arcs that is very minimum, that is, 0.01%.

Fig. 17 is the comprehensive inferencing of the information given in Fig. 6.

2. The time where the highest interaction is achieved is at 1t or 1=hight t , when 100% of

yeast25-cho agents involve in the interaction with DoC = 0.116. On the other hand, the

time where the lowest interaction is achieved is at 11t or 11=lowt t with DoC = 0.035.

Fig. 18 is the comprehensive inferencing of the information given in Fig. 7.

4.2 Estimations based on the knowledge obtained by KGS-based MCC Based on the knowledge obtained by KGS-based MCC regarding the phenomena displayed

by all agents, we can make estimations as follow.

a. The most probable gene that will be playing the important role in the interaction time

between t18 to t24 , with the assumption that the interaction cycle will restart every 17t

times, is gene ASH1. This phenomenon is in line with the information presented in

(http:/ / www.yeastgenome.org/ ) regarding the role of that gene as an inhibitor in

transcription process.

b. Estimation of hight t= 18 and estimation of lowt t= 28

5. Measuring the accurateness of KGS-based MCC results

Validating the results is of importance matter to ensure that the new paradigm we deliver in

this paper is valid. For this purpose we have developed some parameters to compare DoC

values with the number of arcs which is the representation of the existence of

communication paths amongst agents in the influence graphs depicted in previous section.

These parameters are:

a. The number of arcs, ξ and weighted arc, Ξ . Arcs are the arcs that connect the active

agents in each interaction time and are observed by the help of influence graphs.

Weighted arc is normalized value of arc in each interaction time, t or for each gene, g by

the total number of arcs formed in each interaction time, t.

[ ][ ]

1=

Ξ =∑ni

i

i

ξξ

(7)

with 1= ,...,i n and n is the number of genes or one cell cycle, as example 17t.

b. ΔDKJ, Δ% DK , and Δ% _DKJ total . The absolute value of the difference between DoC

and the number of arcs formed at each interaction time, t or for each gene, g. Δ% DK is

the percentage of ΔDKJ while Δ% _DKJ total is the total number of Δ% DK .

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497

[ ] [ ] [ ]Δ = −DKJ i DoC i iξ (8)

[ ] 100Δ = Δ ×% %DKJ DKJ i (9)

1=

Δ = Δ∑% _ %n

i

DKJ total DKJ (10)

with 1= ,...,i n and n is the number of genes or one cell cycle, as example 17t.

c. Behavior match, χ , the total number of match, Χ , and percentage of the behavior

match, Χ% . Parameter that shows the difference of genes behaviour is viewed from

DoC and Ξ with an assumption that the arrangement of genes as given in Table 2 is not

changed. Behaviour matching comparison is done by observing the graphic dynamic

from gene thi to gene thn .

[ ] [ ] [ ][ ] [ ]

1

0

= Ξ⎧⎪= ⎨⎪ ≠ Ξ⎩

,

,

if DoC i i

i

if DoC i i

χ (11)

[ ]1

1=Χ =∑n

i

iχ (12)

[ ]1

1==∑%

n

i

i

Xn

χ (13)

with 1= ,...,i n and n is the number of genes or one cell cycle, as example 17t. [ ]1

iχ is

match gene behaviour otherwise it will be [ ]0

iχ , and %X is the percentage of

behaviour match.

d. Erroneous of behavior match, ε . The percentage of the comparison between the total

number of match of gene behavior, Χ , with the total number of absolute erroneous,

Δ% _DKJ total .

Δ= % _DKJ total

Xε (13)

In this case even though 100=% %X , ε does not always have value of 0% because of

the influence of [ ]ΔDKJ i factor.

On the next tables we will see how these parameters are used to measure the accurateness of

the application of KGS-based MCC to obtain the knowledge regarding the GRS behaviour.

Table 5 contains the system’s knowledge taken from Fig. 17 while Table 6 contains the

system’s knowledge taken from Fig. 18.

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498

thg [ ]DoC i [ ]iξ [ ]Ξ i [ ]ΔDKJ i [ ]Δ% DKJ i [ ]iχ

ACE2 0.031 6 0.026 0.005 0.46 1

ASH1 0.053 12 0.053 0.000 0.01 1

FKH1 0.04 8 0.035 0.005 0.48 1

MBP1 0.044 9 0.040 0.004 0.44 1

MCM1 0.03 7 0.031 0.001 0.08 1

NDD1 0.037 8 0.035 0.002 0.18 1

STB1 0.039 10 0,044 0,005 0,51 1

SWI4 0.045 11 0.048 0.003 0.35 1

SWI5 0.042 8 0.035 0.007 0.68 1

SWI6 0.031 7 0.031 0.000 0.02 1

ALG7 0.029 7 0.031 0.002 0.18 1

CDC20 0.031 8 0.035 0.004 0.42 1

CDC21 0.042 10 0.044 0.002 0.21 1

CDC5 0.042 8 0.035 0.007 0.68 1

CDC6 0.025 6 0.026 0.001 0.14 1

CLB2 0.053 10 0.044 0.009 0.89 0

CLB5 0.052 12 0.053 0.001 0.09 1

CLN1 0.026 7 0.031 0.005 0.48 1

CLN2 0.046 11 0.048 0.002 0.25 1

CTS1 0.041 10 0.044 0.003 0.31 1

EGT2 0.052 12 0.053 0.001 0.09 1

FAR1 0.045 10 0.044 0.001 0.09 1

HTA1 0.029 7 0.031 0.002 0.18 1

PCL2 0.051 12 0.053 0.002 0.19 1

SIC1 0.046 11 0.048 0.002 0.25 1

25 gen 1.002 1 227 0.076 7.63 24

Χ 24

Χ% 96

ε 0.32%

Legend

The most expressive genes based on the results of [ ]iξ

The least expressive genes based on the results of [ ]iξ

Genes with [ ] [ ]≠ ΞDoC i i viewed from [ ]iξ perspective

Table 5. The comparison of individual genes expressiveness for yeast25-cho genes based on

the similarity between DoCs and the number of arcs after 17t of interaction time

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tht [ ]DoC i [ ]iξ [ ]Ξ i [ ]ΔDKJ i [ ]Δ% DKJ i [ ]iχ

1 0.116 25 0.110 0.006 0.59 1

2 0.073 15 0.066 0.007 0.69 1

3 0.054 12 0.053 0.001 0.11 1

4 0.046 11 0.048 0.002 0.25 1

5 0.055 14 0.062 0.007 0.67 1

6 0.052 13 0.057 0.005 0.53 1

7 0.058 14 0.062 0.004 0.37 1

8 0.063 15 0.066 0.003 0.31 1

9 0.072 16 0.070 0.002 0.15 1

10 0.043 9 0.040 0.003 0.34 1

11 0.035 7 0.031 0.004 0.42 1

12 0.052 10 0.044 0.008 0.79 1

13 0.038 9 0.040 0.002 0.16 1

14 0.052 13 0.057 0.005 0.53 1

15 0.058 14 0.062 0.004 0.37 1

16 0.066 15 0.066 0.000 0.01 1

17 0.068 15 0.066 0.002 0.19 1

17t 1.001 227 1 0.06 6.46 17

Χ 17

Χ% 100

ε 0.38

Legend

hight

lowt

Table 6. The behaviour comparison for all yeast25-cho genes based on the similarity

between DoCs and the number of arcs after 17t of interaction time

From the comparison results presented in Table 4 and Table 5, we can conclude as follows.

3. Viewed from the individual genes expressiveness in interaction in 17t times, the

accurateness of system’s result is 24/25 * 100% = 96%, with the erroneous of behaviour

match as much as 0.32%.

4. Viewed from the behaviour of all genes in 17t times of interaction time, the accurateness

of system’s result is 17/17 * 100% = 100%, with the erroneous of behaviour match as

much as 0.38%.

6. The results of the application of KGS-based MCC to other types of yeast25

With the same manner, we apply KGS-based MCC to the other types of yeast25 and the

results are presented in Table 7 for individual gene expressiveness and Table 8 for all genes

behaviour.

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Type Accurateness The Most Expressive Genes Time Interval

Alpha 88% MBP1, CDC5, FAR1 18t

Cdc15 72% ASH1, STB1, CLN2, PCL2 24t

Cdc28 92% CLB5, EGT2 18t

Cho 96% ASH1 17t

Elu 92% SWI6, SIC1 18t

Average 88%

Table 7. The accurateness of the application KGS-based MCC to yeast25 database for

obtaining knowledge regarding the most expressive genes

Interaction Time Type Accurateness

hight lowt

Alpha 100% 5t , 6t 1t

Cdc15 100% 9t , 22t 6t

Cdc28 100% 5t 15t

Cho 100% 1t 11t

Elu 94.4% 6t 13t

Average 98.8%

Table 8. The accurateness of the application KGS-based MCC to yeast25 database for

obtaining knowledge regarding al genes behaviour

Based on the information delivered in the two tables above, we can conclude the

accurateness of KGS-based MCC in obtaining knowledge regarding GRS behaviour as

follows.

1. The average accurateness of the knowledge regarding the most expressive genes

reaches 88%.

2. The averaged accurateness of the knowledge regarding the behaviour of all genes

reaches 98.8%.

7. Conclusion

GRS is a unique system within all living things which regulates the “core“ of living cells

called gene, that is, a sequence of DNA. The regulation performed by GRS to the genes

displays a interesting phenomena that if we can obtain knowledge about them we can use it

to refine the products of the cells in the future. Harmonious with it, in this paper we have

presented in concise manner the process in obtaining knowledge regarding GRS behaviour

by applying KGS-based MCC paradigm on several types of yeast25 database. The core of

KGS-based MCC paradigm is OMA3S information-inferencing fusion method that is

developed primarily for KGS, a new perspective in Artificial Intelligence (Sumari, 2010).

From the strategy as well as the research results we have presented in this paper we can

conclude that the representation of GRS by means of KGS-based MCC paradigm is a very

good approach and very advantegous for obtaining knowledge regarding the behavior of

genes in it. The knowldege includes the most expressive genes and all genes behaviour in a

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501

single cell cycle, that is, a certain interval of interaction time. One example, that is yeast25-

cho, has already been given and the accurateness of the knowledge acquired by the system

is 96% and 100% for having a knowledge of the most expressive genes and all genes

behaviour subsequently. By applying the same technique to other types of yeast25, we

found that in average the knowledge accurateness of the knowledge acquired by the system

is 88% and 98.8% for having a knowledge of the most expressive genes and all genes

behaviour subsequently. These results show that KGS-based MCC paradigm is one of

appropriate means for obtaining knowledge regarding GRS behaviour.

One of our further works will be applying KGS-based MCC paradigm on a larger number of

genes from the same database. We have been conducting a research on this matter and in

the same time perfecting our method so it can be applied to diverse problems.

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Multi-Agent Systems - Modeling, Interactions, Simulations andCase StudiesEdited by Dr. Faisal Alkhateeb

ISBN 978-953-307-176-3Hard cover, 502 pagesPublisher InTechPublished online 01, April, 2011Published in print edition April, 2011

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A multi-agent system (MAS) is a system composed of multiple interacting intelligent agents. Multi-agentsystems can be used to solve problems which are difficult or impossible for an individual agent or monolithicsystem to solve. Agent systems are open and extensible systems that allow for the deployment of autonomousand proactive software components. Multi-agent systems have been brought up and used in severalapplication domains.

How to referenceIn order to correctly reference this scholarly work, feel free to copy and paste the following:

Adang Suwandi Ahmad and Arwin Datumaya Wahyudi Sumari (2011). Obtaining Knowledge of Genes’Behavior in Genetic Regulatory System by Utilizing Multiagent Collaborative Computation, Multi-Agent Systems- Modeling, Interactions, Simulations and Case Studies, Dr. Faisal Alkhateeb (Ed.), ISBN: 978-953-307-176-3,InTech, Available from: http://www.intechopen.com/books/multi-agent-systems-modeling-interactions-simulations-and-case-studies/obtaining-knowledge-of-genes-behavior-in-genetic-regulatory-system-by-utilizing-multiagent-collabora

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